Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

A Note on Central Limit Theorem for Deconvolution Wavelet Density Estimators

  • Lee, Sungho (Department of Statistics, Taegu University)
  • Published : 2002.04.01
Download PDF
⟨ Previous Next ⟩

Abstract

The problem of wavelet density estimation based on Shannon's wavelets is studied when the sample observations are contaminated with random noise. In this paper we will discuss the asymptotic normality for deconvolving wavelet density estimator of the unknown density f(x) when courier transform of random noise has polynomial descent.

Keywords

References

  1. Journal of American Statistics Association v.83 Optimal rates of convergence for deconvoluting a density Carroll, R.J.;Hall, P. https://doi.org/10.2307/2290153
  2. Probability Theory Chow, Y.S.;Teicher, H.
  3. CBMS-MSF Ten Lectures on Wavelets Daubechies, I.
  4. Journal of Royal Statistical Society, Ser. B v.57 Wavelet shrinkage:asymptopia? (with discussion) Donoho, D.;Johnstone, I.;Kerkyacharian, G.;Picard, D.
  5. Annals of Statistics v.24 Density estimation by wavelet thresholding Donoho, D.;Johnstone, I.;Kerkyacharian, G.;Picard, D. https://doi.org/10.1214/aos/1032894451
  6. Annals of Statistics v.19 On the Optimal Rates of Convergence for Nonparametric deconvolution problem Fan, J. https://doi.org/10.1214/aos/1176348248
  7. Sankhya ,Series A v.53 Asymptotic normality for deconvolution kernel density estimators Fan, J.
  8. The Korean Communications in Statistics v.8 A Note on L₁strongly consistent wavelet density estimator for the deconvolution problem Lee, S.
  9. Communications in Statistics: Theory and Methods v.31 no.8 On a strongly consistent wavelet density estimator for the deconvolution problem Lee, S.;Hong, D. H. https://doi.org/10.1081/STA-120006067
  10. Statistics in Medicine v.10 Using empirical Bayes methods on biopharmaceutical research Louis, T.A. https://doi.org/10.1002/sim.4780100604
  11. Annals of Statistics v.27 no.6 Adaptive Wavelet estimator for nonparametric density deconvolution Pensky, M.;Vidakovic, B. https://doi.org/10.1214/aos/1017939249
  12. Communications of Statistics: Theory and Methods v.19 On a strongly consistent nonparametric density estimator for deconvolution problem Taylor, R. L.;Zhang, H. M. https://doi.org/10.1080/03610929008830384
  13. Statistical Modeling by Wavelets Vidakovic, B.
  14. Wavelets and Other Orthogonal Systems with Applications Walter, G. G.
  15. Statistics & Probability Letters v.41 Density estimation in the presence of noise Walter, G. G. https://doi.org/10.1016/S0167-7152(98)00160-6
  16. Statistica Sinica v.2 On deconvolution using time of flight information in positron emission tomography Zhang, H. P.